# Identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80

Identify 19th term of a geometric sequence where a1 = 14 and a9 = 358.80
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scranna0o
The general term of a Geometric Sequence is given by
${a}_{n}=a\cdot {r}^{n-1}$
Where a is the first term also known as ${a}_{1}$ and r is the common ratio.
We have ${a}_{1}$ if we get r we can easily find ${a}_{19}$ by using 19 for n
Let us start by writing the given term using r
${a}_{9}=a\cdot {r}^{8}$
If we divide ${a}_{9}$ by ${a}_{1}$ we would get an equation in r
$\frac{a{r}^{8}}{a}=\frac{358.80}{14}$
${r}^{8}=25.628571428571428571428571428571$
Taking 8th root.
$r=\sqrt[8]{25.628571428571428571428571428571}$
#r=1.4999975504465127405341330547934"
$r\approx 1.5$
${a}_{19}=14{\left(1.5\right)}^{19}$
${a}_{19}=31,035.729480743408203125\text{}$
${a}_{19}\approx 31035.73$